符号中介作为LLM驱动几何推理的语言-数值接口
Symbolic Intermediaries as a Linguistic-Numerical Interface for LLM-Driven Geometric Reasoning
AI总结：
提出符号中介作为连接物理模拟器数值输出与语言模型推理的接口，通过符号回归将连续数值转化为符号表达式，并在协同优化循环中提升几何推理性能。
摘要：
大型语言模型（LLM）在语言和符号对象上展示出推理能力，但直接解释物理模拟器的连续数值输出（例如距离、曲率和轨迹）的能力有限，这些输出难以进行离散分词。在从机构设计到运动规划等空间基础的工程推理任务中，这定义了一个根本性的差距，限制了LLM在更广泛几何领域（例如与物理模拟器接口）的应用。我们提出符号中介，即通过符号回归发现的紧凑解析表达式，作为一种结构化接口，将模拟器的数值轨迹转换为符号形式，语言模型可以解释、比较和批评，同时保留原始几何语义。围绕这个接口，我们构建了一个智能体协调与优化循环：设计智能体将自然语言规范映射为可执行模拟代码，批评智能体基于共享符号词汇进行推理，修订步骤将此反馈转化为基于基础的优化决策，从而实现无需参数更新的推理时泛化。在平面机构综合的MSynth基准上，所有三个评估的LLM智能体比预算匹配的遗传算法基线高出19-53%（带反馈时中位误差降低高达63%），对三种模型架构的批评条目分析表明，该接口将推理从通用结构评论转向基于基础的几何验证。将连续模拟输出转换为符号形式的原理可推广到任何需要以语言方式解释模拟器行为的领域。
英文摘要：
Large Language Models (LLMs) display reasoning capabilities over linguistic and symbolic objects but have limited capabilities to directly interpret the continuous numerical outputs of physics simulators, e.g., distances, curvatures, and trajectories that resist discrete tokenisation. Across spatially grounded engineering reasoning tasks, from mechanism design to motion planning, this defines a fundamental gap, which limits the wider application of LLMs within broader geometrical domains, for exmaple interfacing with physics simulators. We propose symbolic intermediaries, compact analytical expressions discovered via symbolic regression, as a structured interface that translates a simulator's numerical traces into a symbolic form, which language models can interpret, compare, and critique while preserving the original geometric semantics. Around this interface we build an agentic coordination-and-refinement loop: a design agent maps natural-language specifications to executable simulation code, a critique agent reasons over the shared symbolic vocabulary, and a revision step turns this feedback into grounded refinement decisions, enabling inference-time generalization without parameter updates. On the MSynth benchmark for planar mechanism synthesis, all three evaluated LLM agents outperform a budget-matched genetic-algorithm baseline by 19-53% (up to 63% lower median error with feedback), and analysis of the critique entries across three model architectures shows that the interface shifts reasoning from generic structural commentary to grounded geometric verification. The principle of translating continuous simulation outputs into symbolic forms generalises to any domain where simulator behaviour must be interpreted linguistically.
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